FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Derivation of Kolmogorov - Chapman type equations with integrated operator |
Bondrova O.V., Golovko N.I., Zhuk T.A. |
2017, issue 2, P. 135-146 |
Abstract |
| In the work the authors derived equations of Kolmogorov - Chapman type with the integral operator of theoretical and applied importance in the differential equations theory and various applications, for example, of the queueing theory, the population evolution theory, etc. In the work we consider a class of queueing systems with exponential service on one technician device, the input is supplied twice stochastic Poisson flow whose intensity is an spasmodic process at intervals of constancy, distributed according to the exponential law. Models of queueing systems can have the infinite or the final storage device including zero capacity (queueing system with refusals). |
Keywords: equations of Kolmogorov - Chapman type, integral operator, spasmodic process, twice stochastic Poisson stream, queuing system |
Download the article (PDF-file) |
References |
| [1] E. Kamke, Spravochnik po obyknovennym differentsial'nym uravneniiam, Nauka, M, 1976. [2] V.F. Zaitsev, A.D. Polianin, Spravochnik po obyknovennym differentsial'nym uravneniiam, FIZMALIT, M, 2001. [3] A.N. Kolmogorov, Osnovnye poniatiia teorii veroiatnostei, Fazis, M, 1998. [4] A.D. Venttsel', Kurs teorii sluchainykh protsessov, Nauka, M, 1996. [5] C. Karl, Osnovy teorii sluchainykh protsessov, Mir, M, 1973. [6] Iu.B. Germeier, Vvedenie v teoriiu issledovaniia operatsii, Nauka, M, 1971. [7] A. Takha Khemdi, Vvedenie v issledovanie operatsii, Vil'iams, M, 2007. [8] L. Kleinrok, Teoriia massovogo obsluzhivaniia, Mashinostroenie, M, 1979. [9] V.V. Katrakhov, N.I. Golovko, D.E. Ryzhkov, Vvedenie v teoriiu markovskikh dvazhdy stokhasticheskikh sistem massovogo obsluzhivaniia, Izd-vo DVGU, Vladivostok, 2005. [10] I.N. Kovalenko, Teoriia massovogo obsluzhivaniia, Teoriia veroiatnostei. Matematicheskaia statistika. Teoreticheskaia kibernetika, 1971. [11] V.V. Rykov, Upravliaemye sistemy massovogo obsluzhivaniia, Teoriia veroiatnostei. Matematicheskaia statistika. Teoreticheskaia kibernetika, 1975. [12] A.I. Liakhov, “Asimptoticheskii analiz zamknutykh setei ocheredei, vkliuchaiushchikh ustroistva s peremennoi intensivnost'iu obsluzhivaniia”, Avtomatika i telemekhanika, 3, (1997), 131–143. [13] C. Baiocchi, C. Capolo, V. Comincioly, G. Seraggi, “A mathematical model for transient analysis of computer systems”, Performance Evaluation, 3, (1992), 247–264. [14] P.A.W. Lewis, G.S. Shedler, “Statistical analysis of non-stationary series of events in a data base system”, IBM Journal of Research and Development, 20, (1976), 465–482. [15] A. Svoronos, G. Linda, “A convexity result for single-server exponention loss systems with non-stationary arrivals”, J. Appl. Probab., 25, (1988), 224–227. [16] R.A. Upton, S.K. Tripathi, “An approximate transient analysis of the M(t)/M/1 queue”, Performance Evaluation, 2, (1982), 118–132. [17] L.A. Rastrigin, Sovremennye printsipy upravleniia slozhnymi ob"ektami, Sov. radio, M, 1978. [18] Ia.A. Kogan, V.G. Litvin, “K vychisleniiu kharakteristik sistem massovogo obsluzhivaniia s konechnym buferom, rabotaiushchei v sluchainoi srede”, Avtomatika i telemekhanika, 12, (1976), 49–57. [19] N.I. Golovko, V.O. Karetnik, V.E. Tanin, I.I. Safoniuk, “Issledovanie modelei sistem massovogo obsluzhivaniia v informatsionnykh setiakh”, Sibirskii zhurnal industrial'noi Matematiki, 2(34), (2008), 50–64. [20] N.I. Golovko, V.V. Katrakhov, Primenenie modelei SMO v informatsionnykh setiakh, Izd-vo TGEU, Vladivostok, 2008. [21] N.I. Golovko, V.V. Katrakhov, Analiz sistem massovogo obsluzhivaniia, funktsioniruiushchikh v sluchainoi srede, Izd-vo DVGAEU, Vladivostok, 2000, 400. [22] B.V. Gnedenko, Kurs teorii veroiatnostei, Editorial URSS, Moskva, 2005, 448. |